Mathematics
Linear polynomials
रैखिक बहुपद
In this Class 9 Mathematics topic from “Introduction to Polynomials,” students learn how to recognize and work with linear polynomials, whose degree is one and which are commonly written as ax + b, where a is non-zero. They identify the variable, coefficient, constant term, and degree, distinguish linear polynomials from other types, evaluate them for given values, and understand how to find their zero. These ideas build a foundation for simplifying expressions and studying polynomial relationships.
Practice questions
For which value will the zero of ((s-8)x+5s) be (0)?ExpertLevel 33If (p(x)=6x+a) and (q(x)=8x-a), what is (a) if the zero of (p(x)+q(x)) is (-1)?ExpertLevel 33If (p(x)=6x+a) and (q(x)=8x-a), what is (q(x)-p(x))?ExpertLevel 33If (p(x)=ax+6) and (p(p(0))=48), what is (a)?ExpertLevel 33If (p(x)=x+a) and (p(p(4))=16), what is the value of (a)?ExpertLevel 33If (p(x)=mx+n) and (p(-4)=p(2)), when can (p(x)) be linear?ExpertLevel 33In a shop, if \(x\) represents the number of discount coupons, the net amount is \(B(x)=120-8x\). A student calls it a constant polynomial because 120 is a constant number. Which is the correct correction of the student's statement?ExpertLevel 33If (p(x)=12x-5), what is (p(x+2)-p(x-1))?ExpertLevel 33If (p(x)=9x-26), what is the correct value of (p(p(3)))?ExpertLevel 33If (p(x)=13x+a) and (p(p(0))=182), what is the value of (a)?ExpertLevel 33If (p(x)=mx+n), (p(-2)=5) and (p(3)=30), what is (m+n)?ExpertLevel 33If (p(x)=14x-9), what is (p(x+1)+p(x-3))?ExpertLevel 33For which value of r will ((r² − 9r + 20)x + 6) not remain a linear polynomial?MediumLevel 33After simplifying (8(2x-1)-3(5x+4)), which linear polynomial is obtained?ExpertLevel 34If \(p(x)=ax+b\), where \(a\neq 0\) and \(a,b\) are real numbers, is a linear polynomial, which statement about its zeroes is correct?ExpertLevel 34A student writes that the zero of the polynomial \(p(x)=3x+15\) is \(5\). What is the error in the student's solution?ExpertLevel 34If (p(x)=8x-5) and (q(x)=3x+11), what is (2p(x)-5q(x))?ExpertLevel 34For which value will the zero of ((4a-5)x+30) be (-2)?ExpertLevel 34If the zero of (p(x)=ax+b) is (7) and (a=-4), what is (b)?ExpertLevel 34If (p(x)=11x+c) and (p(4)=p(1)+33), what is correct about (c)?ExpertLevel 34